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Abstract

Background

Comorbidity complicates estimations of health-adjusted life expectancy (HALE) using
disease prevalences and disability weights from Burden of Disease studies. Usually,
the exact amount of comorbidity is unknown and no disability weights are defined for
comorbidity.

Methods

Using data of the Dutch national burden of disease study, the effects of different
methods to adjust for comorbidity on HALE calculations are estimated. The default
multiplicative adjustment method to define disability weights for comorbidity is compared
to HALE estimates without adjustment for comorbidity and to HALE estimates in which
the amount of disability in patients with multiple diseases is solely determined by
the disease that leads to most disability (the maximum adjustment method). To estimate
the amount of comorbidity, independence between diseases is assumed.

Results

Compared to the multiplicative adjustment method, the maximum adjustment method lowers
HALE estimates by 1.2 years for males and 1.9 years for females. Compared to no adjustment,
a multiplicative adjustment lowers HALE estimates by 1.0 years for males and 1.4 years
for females.

Conclusion

The differences in HALE caused by the different adjustment methods demonstrate that
adjusting for comorbidity in HALE calculations is an important topic that needs more
attention. More empirical research is needed to develop a more general theory as to
how comorbidity influences disability.

Background

Health-adjusted life expectancy (HALE) is a summary measure of population health that
has been introduced as part of the Health Expectancy Network (Réseau Espérance de
Vie en Santé, or REVES) and is defined as: "a generic term for a weighted expectation of life summed over a complete set of health
states" [1]. HALE, like life expectancy, is independent of the size and composition of the population
and is therefore useful to make comparisons between populations and over time [2]. One method of estimating HALE is by using data available from Burden of Disease
studies [3]. As a first step to estimate HALE from Burden of Disease data, disease prevalences
are coupled to disease specific disability weights to estimate the average amount
of disability in a population specified by sex and age [4]. Disability weights reflect the relative severity and impact of a disease and theoretically
range from 0 (no disability) to 1 (death) [5]. Then, the average amount of disability can be combined with a life table to estimate
HALE. In this paper, we will focus on this specific form of HALE that has also been
termed disability-adjusted life expectancy (DALE) [3,4].

Comorbidity, defined as the presence of two or more diseases in one person, complicates
HALE calculations for two reasons. The first one is that the exact amount of comorbidity
is unknown since all data on disease incidence, prevalence and mortality gathered
in Burden of Disease (BOD) studies are disease specific [6]. The second reason is that there are no disability weights defined for comorbidity
[6]. In a previous study, Barendregt and Bonneux found that HALE was generally insensitive
to different methods to define disability weights for comorbidity [7]. However, they limited their research to six diseases and to comorbidity between
disease pairs only. In this article, we will examine the impact of different methods
to define disability weights for comorbidity on HALE estimates and compare them with
HALE estimations without adjustment for comorbidity.

If burden of disease data and disability weights are used for calculations of HALE,
disability weights for comorbidity are usually calculated assuming a multiplicative
model [4,8]. The multiplicative model implies that disability increases with the number of conditions
one has, but that the overall effect is less than additive. This is in line with findings
of Verbrugge et al. [9]. They tested whether disability increased linearly with the number of chronic conditions
individuals have and investigated whether there are interaction effects on disability
for specific combinations of chronic diseases. They concluded that although disability
increases as the number of chronic conditions increases, the marginal increase decreased
as the number of conditions increases. However, they also found that in many cases
the disability caused by having two diseases was not higher than having either one
of the two diseases. This latter finding suggests that solely the disease that leads
to most disability determines the total amount of disability in patients with multiple
diseases. To investigate the effect of adjustments for comorbidity we estimated HALE
using two different methods to define disability weights for comorbidity:

- multiplicative adjustment method: using this method it is assumed that the impact
on disability due to comorbidity is proportional. Although disability increases with
additional diseases, it is less than the sum of disability weights for the individual
diseases. This is the default method used in HALE calculations [4,8];

- maximum adjustment method: using this method the disability weight for comorbidity
equals the disability weight of the disease with the highest disability weight. This
adjustment for comorbidity can be thought of as a maximum adjustment since having
multiple diseases only leads to more disability if individual diseases lead to more
disability. The total amount of disability attributed to comorbidity is equal to the
highest amount of disability associated with one of the concurrent diseases.

To quantify the importance of comorbidity adjustments, we will use HALE estimates
without adjustments for comorbidity as a comparator. In the next section, we describe
how to estimate the average disability weight and HALE using the different adjustment
methods if independence between diseases is assumed. Then, results of HALE estimates
are presented. In the last section, implications of the results and directions for
future research are discussed.

Methods

In order to estimate HALE we set up an abridged life table using mortality rates for
the Netherlands from 1999 [10]. The number of life years obtained from the life table were multiplied by one minus
the average disability weights:

HALEg,a, health-adjusted life expectancy gender g age a

Lg,a number of life years lived between age a and a+5 for gender g

Lg,85+ number of life years lived after age 85 for gender g

mg,a average disability weight between age a and a+5 for gender g

mg,85+ average disability weight after age 85+ for gender g

lg,a number of survivors at age a in the life table cohort for gender g

z last open-ended age interval in the life table

Age and sex specific average disability weights are a function of disease specific
prevalence rates and disability weights. In our study, data from the Dutch Burden
of Disease Study was used to estimate average disability weights. The Dutch Burden
of Disease Study estimated disability weights, using a large panel of experts and
the person trade off method [11], and disease prevalence of 48 different disease categories [12]. All data used in our calculations (mortality rates, disease prevalences and disability
weights) are available in 1.

To estimate comorbidity prevalence, independence between diseases is assumed so the
amount of comorbidity between disease 1 and 2 (the joint prevalence of diseases 1
and 2) is simply the product of their prevalence rates:

Gender-specific average disability weights were calculated using age classes of five
years (0–4, 5–9, 10–14 to 85+). However, for notational simplicity, age and sex indices
have been omitted in the notation.

No adjustment for comorbidity

When no adjustment for comorbidity is made the average disability weight can be calculated
by simply adding up the disability caused by all diseases:

m average disability weight

pd prevalence rate of disease d

wd disability weight of disease d

Making no adjustment for comorbidity is equivalent to assuming that effects of comorbidity
on disability are additive. Thus, if a person has more than one disease his total
disability weight equals the sum of the disability weights for those diseases. However,
in this interpretation individual disability weights may add up to more than one.
This cannot be interpreted in a plausible way because it would imply that more than
one year of health is lost when living for one year with those diseases.

Multiplicative adjustment method

Using this method, it is assumed that the increase in disability due to comorbidity
disability is proportional. Total disability for an individual having more diseases
can be written as:

w(1,2) disability weight of an individual with disease 1 and 2

w(d) disability weight of an individual with d diseases

This implies that the disability due to comorbidity increases with more comorbid diseases
but is less than the sum of individual disability weights for all comorbid diseases.
If there are only 2 diseases the average disability weight assuming independence equals:

Maximum adjustment method

Compared to having one disease, having two diseases only leads to more disability
if the second disease causes more disability than the first one. Assuming that the
diseases are ordered in terms of disability weights, e.g. w1≥w2≥w3............wn someone who has disease 1 and 2 has a disability weight that equals that of w1 since disease 1 is worse than disease 2:

In order to estimate average disability weights using this method the prevalence rate
for which disease d has the highest disability weight must be estimated (denoted Hd). We can recursively define the prevalence rate Hd (see Appendix for a derivation):

Hd prevalence rate for which disease d has the highest disability weight

The average disability weight can then be written as:

Comparing different methods to adjust for comorbidity

Compared to no adjustment, the multiplicative adjustment method results in a lower
average disability weight but compared to the maximum adjustment method in a higher
average disability weight:

For d diseases:

Results

Figures 1 and 2 display the estimated average disability weights for men and women, using the different
adjustment methods.

Figure 1. Average disability weights for men in the Netherlands 1999 using different methods
to adjust for comorbidity.

Figure 2. Average disability weights for women in the Netherlands 1999 using different methods
to adjust for comorbidity.

By definition, the maximum adjustment method results in the lowest estimate of the
average disability weight and no adjustment for comorbidity in the highest estimate.
The difference between the adjustment methods increases with age. This is caused by
the higher amount of comorbidity in the elderly. At age 85 and over the difference
in the average disability weight between the multiplicative adjustment method and
no adjustment amounts to 0.11 for men and 0.14 for women. The difference between the
multiplicative and maximum adjustment methods are 0.11 and 0.13 for respectively men
and women aged 85 and over. Thus, the choice for adjustment method has more implications
in an elderly population than in a younger population.

Tables 1 and 2 display estimates of life expectancy and HALE. Life expectancy for Dutch males in
1999 was 75.9 years. Depending on the adjustment method for comorbidity, 65.7 to 67.9
years are considered healthy years. Females have a higher life-expectancy, and also
a higher HALE. Independent of the method of adjustment, women's HALE, relative to
life expectancy, is always lower than men's HALE. This reflects the fact that men
more often than women die from lethal diseases with a short duration (e.g. lung cancer).
At birth, the difference in HALE between the multiplicative and maximum adjustment
method is 1.2 years for males and 1.9 years for females. For males, the difference
in HALE between the multiplicative and maximum adjustment method declines from 1.2
years at birth to 1.0 at the age of 60. For females, the differences between the methods
are somewhat larger. The difference of 1.9 years in HALE at birth between the multiplicative
and maximum adjustment method declines to 1.6 at the age of 60. For both males and
females at all ages, the differences between no adjustment and multiplicative adjustment
are smaller than the differences between the multiplicative and maximum adjustment
method.

Discussion and conclusion

In this study, two different methods to adjust for comorbidity in HALE calculations
were compared to HALE estimates without adjustment for comorbidity. The methods differ
in the manner in which disability weights for comorbid conditions were defined. The
multiplicative adjustment method implies that comorbidity increases disability but
that the effects are less than the sum of disability from the individual diseases.
Using the maximum adjustment method, disability is solely determined by the most severe
disease. Compared to no adjustment, a multiplicative adjustment lowers HALE estimates
with 1.0 years for males and 1.4 years for females. The maximum adjustment methods
lowers HALE estimates compared to the multiplicative adjustment with 1.2 years for
males and 1.9 years for females. Thus, the differences in HALE resulting of differences
in defining disability weights are larger than the differences between no adjustment
and the multiplicative adjustment method. Although we think the differences in HALE
resulting of the different methods to define disability weights are important, also
uncertainly related to the estimation of the prevalence of each of the 48 diseases
may cause substantial variations in the average disability weights and, therefore,
on HALE estimates. However, it is difficult to quantify this uncertainty because uncertainty
estimates around the disease prevalence are not available [12]. In an attempt to test the sensitivity of HALE for variations in prevalence rates
we calculated HALE using the multiplicative adjustment method and increased all prevalence
rates with 10%. This lowered HALE estimates with less than one year for both males
and females.

Contrary to our results, Barendregt and Bonneux found in a previous study that HALE
was generally insensitive to different methods of weighing comorbidity [7]. However, they limited themselves to six diseases and to comorbidity between disease
pairs only. In our study, all possible combinations of comorbidity between 48 diseases
were investigated. The explanation for the difference in results between our study
and the Barendregt and Bonneux study is straightforward: if more diseases are taken
into account, there is more comorbidity, especially if comorbidity between all disease
combinations is described. With a higher prevalence of comorbidity, the method used
to adjust for comorbidity becomes more important.

A crucial assumption in this paper is that of independence between diseases. Although
this assumption may be violated in practice, it will not influence our conclusion
that adjustments for comorbidity are important in HALE calculations. In fact, assuming
independence probably underestimates the amount of comorbidity since the probability
of getting different diseases is not independent due to clustering of diseases as
a result of genetics, biological risk factors (e.g. blood pressure, cholesterol) environmental
factors (e.g. air pollution) and lifestyle (e.g. smoking and drinking) [13,14].

Different methods to define disability weights for comorbidity can have important
implications not only for the estimation of HALE itself but also on applications of
HALE such as monitoring trends in health or as an aid in priority setting. Even if
the same methodology to adjust for comorbidity is used consistently, the choice of
the adjustment method might influence the manner in which HALE reacts to trends or
interventions. For instance, when using the maximum adjustment method eliminating
diseases with low disability weights has smaller or even no impact on HALE compared
to the multiplicative adjustment method. Furthermore, both the maximum and multiplicative
adjustment methods imply that in priority setting, ceteris paribus, less priority
should be given to patients with more comorbidity. For example, improving diabetes
care in diabetes patients without coronary heart disease results in a larger increase
in average disability than diabetes care in patients with coronary heart disease.
This latter example demonstrates that the choice for comorbidity adjustment might
also have implications for equity trade-offs. Moreover, for the comparison of effects
of specific interventions targeted at groups with different comorbidity prevalences
(e.g. young and old), the choice of adjustment method may have a different impact
for different interventions, and thus may affect the conclusion.

The problems caused by comorbidity in HALE calculations are not present if self reported
generic measures of health such as the EQ-5D are used. [15-17] Then, patients decide for themselves how the total disability that is caused by all
concurrent diseases influences their functioning and quality of life. Therefore, empirical
results of studies using self reported generic measures could be used to develop a
more general theory as to how comorbidity influences disability. For instance, a question
that needs to be answered is whether two comorbid diseases from different "disease
clusters" (such as a physically limiting disease combined with a mental disease) leads
to more disability than two or more diseases from one "disease cluster". Such a theory
might be used to justify the choice for a specific adjustment method in HALE calculations.

Competing interests

The author(s) declare that they have no competing interests.

Authors' contributions

PHMvB carried out the analyses and drafted the manuscript. RTH contributed to the
mathematics. NH provided the data. All authors contributed to the writing of the paper.

Appendix: derivation of average disability weights for maximum adjustment method

The fraction of the population that gets the weight of disease d equals the prevalence rate of disease d minus the fraction of the population that has disease d but also a disease with a higher disability weight. Assuming that the diseases are
ordered in terms of disability weights, e.g. w1≥w2≥w3 .....................wn we can write this principle for three diseases as:

H1 = p1

H2 = p2 *(1 - p1)

H3 = p3 *(1 - (p1 + p2 - p2 * p2))

Hd prevalence rate for which disease d has the highest disability weight

pd prevalence rate of disease d

This can be rewritten to:

H1 = p1

H2 = (1 - H1) p2

H3 = (1 - H1 - H2) p3

Using this we can recursively define the prevalence rate Hd:

The average disability weight can then be written as:

m average disability weight

wd disability weight of disease d

References

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Contribution of the Network on Health Expectancy and the Disability Process to The
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